Problem: Simplify the following expression: $y = \dfrac{5p^2 + 25p - 180}{p - 4} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $5$ , so we can rewrite the expression: $ y =\dfrac{5(p^2 + 5p - 36)}{p - 4} $ Then we factor the remaining polynomial: $p^2 + {5}p {-36} $ ${-4} + {9} = {5}$ ${-4} \times {9} = {-36}$ $ (p {-4}) (p + {9}) $ This gives us a factored expression: $\dfrac{5(p {-4}) (p + {9})}{p - 4}$ We can divide the numerator and denominator by $(p + 4)$ on condition that $p \neq 4$ Therefore $y = 5(p + 9); p \neq 4$